Two-dimensional quantum walk with non-Hermitian skin effects

• URL: http://arxiv.org/abs/2005.09474v2
• Date: Tue, 2 Mar 2021 12:36:36 GMT
• Title: Two-dimensional quantum walk with non-Hermitian skin effects
• Authors: Tianyu Li, Yong-Sheng Zhang, and Wei Yi
• Abstract summary: We show that the emergence of topological edge states are consistent with Floquet winding numbers calculated using a non-Bloch band theory. Our work would stimulate further studies of non-Hermitian Floquet topological phases where skin effects play a key role.
• Score: 7.182858821473896
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We construct a two-dimensional, discrete-time quantum walk exhibiting non-Hermitian skin effects under open-boundary conditions. As a confirmation of the non-Hermitian bulk-boundary correspondence, we show that the emergence of topological edge states are consistent with Floquet winding numbers calculated using a non-Bloch band theory invoking time-dependent generalized Billouin zones. Further, the non-Bloch topological invariants associated with quasienergy bands are captured by a non-Hermitian local Chern marker in real space, defined through local biorthogonal eigen wave functions of the non-unitary Floquet operator. Our work would stimulate further studies of non-Hermitian Floquet topological phases where skin effects play a key role.

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